Elements Of Modern Algebra
8th Edition
ISBN: 9781285463230
Author: Gilbert, Linda, Jimmie
Publisher: Cengage Learning,
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Chapter 6.1, Problem 4E
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Compare the interest earned from #1 (where simple interest was used) to #5 (where compound interest was used). The principal, annual interest rate, and time were all the same; the only difference was that for #5, interest was compounded quarterly. Does the difference in interest earned make sense? Select one of the following statements. a. No, because more money should have been earned through simple interest than compound interest. b. Yes, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. c. No, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. d. Yes, because more money was earned when compounded quarterly. For compound interest you earn interest on interest, not just on the amount of principal.
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Chapter 6 Solutions
Elements Of Modern Algebra
Ch. 6.1 - True or False
Label each of the following...Ch. 6.1 - Label each of the following statements as either...Ch. 6.1 - True or false
Label each of the following...Ch. 6.1 - Label each of the following statements as either...Ch. 6.1 - Label each of the following statements as either...Ch. 6.1 - True or false
Label each of the following...Ch. 6.1 - True or false
Label each of the following...Ch. 6.1 - Label each of the following statements as either...Ch. 6.1 - Exercises Let I be a subset of ring R. Prove that...Ch. 6.1 - Prob. 2E
Ch. 6.1 - Prove or disprove each of the following...Ch. 6.1 - Exercises
If and are two ideals of the ring ,...Ch. 6.1 - Prob. 5ECh. 6.1 - Exercises
Find two ideals and of the ring such...Ch. 6.1 - Exercises
Let be an ideal of a ring , and let be...Ch. 6.1 - Exercises
If and are two ideals of the ring ,...Ch. 6.1 - Find the principal ideal (z) of Z such that each...Ch. 6.1 - Let I1 and I2 be ideals of the ring R. Prove that...Ch. 6.1 - Find a principal ideal (z) of such that each of...Ch. 6.1 - 12. Let be a commutative ring with unity. If...Ch. 6.1 - 13. Verify each of the following statements...Ch. 6.1 - 14. Let be an ideal in a ring with unity . Prove...Ch. 6.1 - Let I be an ideal in a ring R with unity. Prove...Ch. 6.1 - Prove that if R is a field, then R has no...Ch. 6.1 - In the ring of integers, prove that every subring...Ch. 6.1 - Let a0 in the ring of integers . Find b such that...Ch. 6.1 - 19. Let and be nonzero integers. Prove that if and...Ch. 6.1 - 20. If and are nonzero integers and is the least...Ch. 6.1 - Prove that every ideal of n is a principal ideal....Ch. 6.1 - 22. Let . Prove .
Ch. 6.1 - 23. Find all distinct principal ideals of for the...Ch. 6.1 - 24. If is a commutative ring and is a fixed...Ch. 6.1 - Given that the set S={[xy0z]|x,y,z} is a ring with...Ch. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - 28. a. Show that the set is a ring with respect to...Ch. 6.1 - 29. Let be the set of Gaussian integers . Let .
...Ch. 6.1 - a. For a fixed element a of a commutative ring R,...Ch. 6.1 - Let R be a commutative ring that does not have a...Ch. 6.1 - 32. a. Let be an ideal of the commutative ring ...Ch. 6.1 - 33. An element of a ring is called nilpotent if...Ch. 6.1 - 34. If is an ideal of prove that the set is an...Ch. 6.1 - Let R be a commutative ring with unity whose only...Ch. 6.1 - 36. Suppose that is a commutative ring with unity...Ch. 6.2 - True or false
Label each of the following...Ch. 6.2 - True or false
Label each of the following...Ch. 6.2 - Label each of the following statements as either...Ch. 6.2 - Label each of the following statements as either...Ch. 6.2 - Label each of the following statements as either...Ch. 6.2 - Label each of the following statements as either...Ch. 6.2 - Each of the following rules determines a mapping...Ch. 6.2 - 2. Prove that is commutative if and only if is...Ch. 6.2 - 3. Prove that has a unity if and only if has a...Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Assume that the set S={[xy0z]|x,y,z} is a ring...Ch. 6.2 - Assume that the set R={[x0y0]|x,y} is a ring with...Ch. 6.2 - 9. For any let denote in and let denote in .
a....Ch. 6.2 - Let :312 be defined by ([x]3)=4[x]12 using the...Ch. 6.2 - 11. Show that defined by is not a homomorphism.
Ch. 6.2 - 12. Consider the mapping defined by . Decide...Ch. 6.2 - Prob. 13ECh. 6.2 -
14. Let be a ring with unity . Verify that the...Ch. 6.2 - In the field of a complex numbers, show that the...Ch. 6.2 - Prob. 16ECh. 6.2 - Define :2()2(2) by ([abcd])=[[a][b][c][d]]. Prove...Ch. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - 25. Figure 6.3 gives addition and multiplication...Ch. 6.2 - Prob. 26ECh. 6.2 - 27. For each given value of find all homomorphic...Ch. 6.2 - Prob. 28ECh. 6.2 - 29. Assume that is an epimorphism from to ....Ch. 6.2 - 30. In the ring of integers, let new operations of...Ch. 6.2 - Prob. 31ECh. 6.3 - True or False
Label each of the following...Ch. 6.3 - Prob. 2TFECh. 6.3 - True or False
Label each of the following...Ch. 6.3 - True or False
Label each of the following...Ch. 6.3 - Prob. 5TFECh. 6.3 - Find the characteristic of each of the following...Ch. 6.3 - Find the characteristic of the following rings. 22...Ch. 6.3 - 3. Let be an integral domain with positive...Ch. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - 8. Prove that the characteristic of a field is...Ch. 6.3 - Let D be an integral domain with four elements,...Ch. 6.3 - Let R be a commutative ring with characteristic 2....Ch. 6.3 -
11. a. Give an example of a ring of...Ch. 6.3 - 12. Let be a commutative ring with prime...Ch. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - 15. In a commutative ring of characteristic 2,...Ch. 6.3 - A Boolean ring is a ring in which all elements x...Ch. 6.3 - 17. Suppose is a ring with positive...Ch. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.3 - Let I be the set of all elements of a ring R that...Ch. 6.3 - 21. Prove that if a ring has a finite number of...Ch. 6.3 - 22. Let be a ring with finite number of...Ch. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - Prob. 25ECh. 6.3 - Prove that every ordered integral domain has...Ch. 6.4 - Label each of the following statements as either...Ch. 6.4 - Prob. 2TFECh. 6.4 - According to part a of Example 3 in Section 5.1,...Ch. 6.4 - Let R be as in Exercise 1, and show that the...Ch. 6.4 - Prob. 3ECh. 6.4 - Show that the ideal is a maximal ideal of .
Ch. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Find all maximal ideals of .
Ch. 6.4 - Find all maximal ideals of 18.Ch. 6.4 - Let be the ring of Gaussian integers. Let
...Ch. 6.4 - Let R bethe ring of Gaussian integersas an...Ch. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - Find all prime ideals of .
Ch. 6.4 - Find all prime ideals of .
Ch. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - . a. Let, and . Show that and are only ideals...Ch. 6.4 - 27. If is a commutative ring with unity, prove...Ch. 6.4 - If R is a finite commutative ring with unity,...
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- If $8000 is deposited into an account earning simple interest at an annual interest rate of 4% for 10 years, howmuch interest was earned? Show you work.arrow_forward10-2 Let A = 02-4 and b = 4 Denote the columns of A by a₁, a2, a3, and let W = Span {a1, a2, a̸3}. -4 6 5 - 35 a. Is b in {a1, a2, a3}? How many vectors are in {a₁, a₂, a3}? b. Is b in W? How many vectors are in W? c. Show that a2 is in W. [Hint: Row operations are unnecessary.] a. Is b in {a₁, a2, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. ○ A. No, b is not in {a₁, a2, 3} since it cannot be generated by a linear combination of a₁, a2, and a3. B. No, b is not in (a1, a2, a3} since b is not equal to a₁, a2, or a3. C. Yes, b is in (a1, a2, a3} since b = a (Type a whole number.) D. Yes, b is in (a1, a2, 3} since, although b is not equal to a₁, a2, or a3, it can be expressed as a linear combination of them. In particular, b = + + ☐ az. (Simplify your answers.)arrow_forward14 14 4. The graph shows the printing rate of Printer A. Printer B can print at a rate of 25 pages per minute. How does the printing rate for Printer B compare to the printing rate for Printer A? The printing rate for Printer B is than the rate for Printer A because the rate of 25 pages per minute is than the rate of for Printer A. pages per minute RIJOUT 40 fy Printer Rat Number of Pages 8N WA 10 30 20 Printer A 0 0 246 Time (min) Xarrow_forward
- OR 16 f(x) = Ef 16 χ по x²-2 410 | y = (x+2) + 4 Y-INT: y = 0 X-INT: X=0 VA: x=2 OA: y=x+2 0 X-INT: X=-2 X-INT: y = 2 VA 0 2 whole. 2-2 4 y - (x+2) = 27-270 + xxx> 2 क् above OA (x+2) OA x-2/x²+0x+0 2 x-2x 2x+O 2x-4 4 X<-1000 4/4/2<0 below Of y VA X=2 X-2 OA y=x+2 -2 2 (0,0) 2 χarrow_forwardI need help solving the equation 3x+5=8arrow_forwardWhat is the domain, range, increasing intervals (theres 3), decreasing intervals, roots, y-intercepts, end behavior (approaches four times), leading coffiencent status (is it negative, positivie?) the degress status (zero, undifined etc ), the absolute max, is there a absolute minimum, relative minimum, relative maximum, the root is that has a multiplicity of 2, the multiplicity of 3.arrow_forward
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